Question: Consider the following signals: xo(t) 21(t) x(t) = = { 0 { { 0 cos (+) if te [0, T otherwise cos(+5) cos(+) if

Consider the following signals: xo(t) x(t) x(t) = = { 0 { { 0 cos (7+) if te [0, T otherwise cos(27+5)if te

Consider the following signals: xo(t) 21(t) x(t) = = { 0 { { 0 cos (+) if te [0, T otherwise cos(+5) cos(+) if te [0, T] otherwise if te [0, T] otherwise a. Find a set of orthonormal basis functions for this signal set. Show that they are orthonormal. Hint: Use the identity for cos(a + b) = cos(a) cos(b) sin(a) sin(b). (4 pts) b. Find the data symbols corresponding to the signals above for the basis functions you found in (a). (3 pts) c. Find the following inner products: (3 pts) (i) < xo(t), ro(t) > (ii) < xo(t), ai(t) > (iii) < xo(t), (t) >

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